Casimir-Lifshitz Interaction between Dielectrics of Arbitrary Geometry: A Dielectric Contrast Perturbation Theory

TL;DR

This paper develops a perturbation theory based on dielectric contrast to calculate Casimir-Lifshitz forces for arbitrary dielectric geometries, extending existing methods by focusing on dielectric properties rather than geometry.

Contribution

It introduces a dielectric contrast perturbation approach to evaluate electromagnetic fluctuation forces for complex dielectric shapes, complementing geometric perturbation methods.

Findings

Recasts Lifshitz energy as a sum of many-body contributions.

Discusses the validity and convergence of the perturbation theory.

Provides example calculations for parallel semi-infinite objects.

Abstract

The general theory of electromagnetic--fluctuation--induced interactions in dielectric bodies as formulated by Dzyaloshinskii, Lifshitz, and Pitaevskii is rewritten as a perturbation theory in terms of the spatial contrast in (imaginary) frequency dependent dielectric function. The formulation can be used to calculate the Casimir-Lifshitz forces for dielectric objects of arbitrary geometry, as a perturbative expansion in the dielectric contrast, and could thus complement the existing theories that use perturbation in geometrical features. We find that expansion in dielectric contrast recasts the resulting Lifshitz energy into a sum of the different many-body contributions. The limit of validity and convergence properties of the perturbation theory is discussed using the example of parallel semi-infinite objects for which the exact result is known.